The excitation of magnetohydrodynamic (MHD) and resonant instabilities and their effect on the plasma profiles during the current ramp-up phase of a beam-driven JT-60SA tokamak plasma is studied using the MHD-PIC hybrid code MEGA. In the simple scenario considered, the plasma is only driven by one negative-ion-based neutral beam, depositing 500 keV deuterons at 5 MW power off-axis at about mid-radius. The beam injection starts half-way in the ramp-up phase. Within 1 s, the beam-driven plasma current and fast ion pressure produce a configuration that is strongly unstable to rapidly growing MHD and resonant modes. Using MEGA, modes with low toroidal mode numbers in the range n=1-4 are examined in detail and shown to cause substantial changes in the plasma profiles. The necessity to develop reduced models and incorporate the effects of such instabilities in integrated codes used to simulate the evolution of entire plasma discharges is discussed.